An inverted image is magnified by 2 when the object is placed 22cm in front of a concave mirror. Determine the image distance and the focal length
di=44 yo
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To determine the image distance and focal length of a concave mirror when an inverted image is magnified by 2, we can use the mirror/ lens equation:
1/f = 1/dᵢ + 1/dₒ
where:
f = focal length of the mirror
dᵢ = image distance (distance of the image from the mirror)
dₒ = object distance (distance of the object from the mirror)
Given that the object distance (dₒ) is 22 cm and the magnification factor is 2, we can set up the following equation:
2 = -dᵢ / dₒ
Since the image is inverted, the magnification factor will be negative.
Solving for dᵢ using the equation above:
2 = -dᵢ / 22
Multiplying both sides by 22, we get:
44 = -dᵢ
Therefore, the image distance (dᵢ) is -44 cm. The negative sign indicates that the image is formed on the same side as the object (in front of the mirror).
Now, we can use the mirror/ lens equation to find the focal length (f) of the mirror:
1/f = 1/dᵢ + 1/dₒ
1/f = 1/-44 + 1/22
Simplifying,
1/f = (-1 + 2) / 44
1/f = 1 / 44
Therefore, the focal length (f) of the concave mirror is 44 cm.
An inverted image is magnified twice when the object is placed 22cm in front of a concave mirror. Determine image distance and focal length of the mirror.
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